CAIRO — Egypt’s military rulers said Thursday that parliamentary elections starting next week will he held on schedule despite spreading unrest.

The military also rejected protesters’ demands that it immediately step down, saying that doing so would amount to a “betrayal” of the people’s trust and arguing that the military took over from ousted president Hosni Mubarak by popular demand.

“Let me just say this: There will be no postponement in the election,” said Maj. Gen. Mamdouh Shaheen, one of two members of the ruling military council who spoke during a televised news conference. “The elections will be held on time with all of its three stages held on schedule.”

The comments suggested that the military council led by Field Marshal Hussein Tantawi has no intention of making more concessions under pressure from tens of thousands of protesters gathered in Cairo’s Tahrir Square, which was the epicenter of the 18-day uprising that toppled Mubarak nine months ago.

Earlier Thursday, police and protesters agreed to a truce negotiated by Muslim clerics after five days of fierce street battles that have left nearly 40 dead.

Another council member, Maj. Gen. Mukhtar el-Mallah, added that Egyptians must “focus” on the elections, rather than street protests.

Protests demanding that the military rulers step down have spiraled into a week of violence as Egyptian police battled with demonstrators, blanketing the area around Tahrir Square with tear gas.

That has deepened the country’s economic and security woes and raised doubts about the ability of the country’s interim leaders to hold the first parliamentary elections since Mubarak’s regime was toppled. Voting is scheduled to begin on Monday and will be staggered over three months.

El-Mallah insisted the military’s immediate resignation would amount to a “betrayal of the trust placed in our hands by the people.” He later said the throngs in Tahrir did not represent the whole of Egypt. “We will not relinquish power because of a slogan-chanting crowd ... Being in power is not a blessing. It is a curse. It’s a very heavy responsibility.”